# Pascal's Triangle

n =
+ 1 rows

Numbers

Binomial Coefficients

Numbers

Binomial Coefficients

n =
+ 1 rows

Numbers

Binomial Coefficients

Numbers

Binomial Coefficients

Choose the number of rows to display (capped at 30+1) and whether you'd like the cells to be labeled with binomial coefficients or the integer value of the coefficient. Then, choose which property to explore:

**Play Sums**

Watch the triangle's construction by sums. The outer cells of the triangle are labeled 1. Each interior cell is the sum of the two cells immediately above it.**Play Hockey**

Click on an outer cell. The possible interior entries to choose from on the associated diagonal will be highlighted. Click on any of these interior entries to see the hockey stick property.**Play Sierpinski**

See the entries of the triangle shaded by parity. In the applet, the odd valued cells will be darkened and even valued cells will remain white. The effect is particularly striking when at least 20 rows are displayed.**Play Triangular**

Highlight the sequence of triangular numbers, found on the third diagonals of Pascal's triangle.**Play Squares**

Reveal the sequence of square numbers hidden in the triangle, formed by the sum of adjacent triangular numbers on the third diagonal.**Play Primes**

Highlight the primes found on the second diagonals. Note that if a prime is found, every interior cell's value in that row will be divisible by the prime.**Reset**

Clear the triangle.

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.